language: This lecture is given in German in both semesters and in English in winter semester only.

schedule for WS 2017/18:

Wed, 14:00, HS 2 + Th, 17:00, HS 3

Tutorial: Wed, 12:30, HS 2

focus of this lecture

This lecture gives the mathematical fundamentals for further study in all IT related programs. The contents are highly related to a lot of parallel and subsequent courses. This lecture does not require any knowledge of programming.

This lecture covers standard material such as logics and proof concepts, set theory, number theory, combinatorics, and graph theory. Furthermore, we give an introduction in group and field theory which highlights in the construction algorithm for arbitrary finite fields. For exercises, some construction programs implemented by students of FH Wedel in a software project may be downloaded here (instructions in German).

This lecture is complemented by exercises lead by teaching assistants.

content of teaching

The following links show the slides and the assignments of the course held in WS 2016/17. Updates in WS 2017/18 may occur continuously and will be indicated by a red update information. Students enrolled at FH Wedel will find all assignments and some student solutions on the handout server.

(Examples for gcd and lcm, PrimeFactorisation with Maxima)Note for the factorisation file: You must store this with the extension .wxm (not .txt). This file can the be executed and altered by the open-source tool Maxima (download here for all operating systems or here an older but still functioning version on the handout server for Windows). Warning: The file should not be altered by any editor other tha Maxima's!

references

English books with partial coverage of this lecture (see slide references) or for further concentration:

Norman L. Biggs: Discrete Mathematics, Oxford University Press 2002 (2. edition), ISBN 0-19-850717-8This book covers nearly all material of this lecture in a slightly more mathematical manner except for some graph algorithms. This book also covers a a lot of material not discussed in this lecture.

Neville Dean: The Essence of Discrete Mathematics, Prentice Hall 1997, ISBN 0-1334-5943-8This book covers the first 2 chapters of this lecture entirely on a more elementary level.

Susanna S. Epp: Discrete Mathematics with Applications, Brooks/Cole 1995 (2. edition), ISBN 0-534-94446-9This book covers most of this lecture (Chapter 5 not at all), some on a more elementary level, and lays a strong focus in algorithmic applications.

Jiri Matousek / Jaroslav Nesetril: An Invitation to Discrete Mathematics, Oxford University Press 2008 (2. edition), ISBN 0-1985-7042-2This book covers some of the material of this lecture on a more scientific level and a lot of other issues for broadening the horizon.

Kenneth H. Rosen: Discrete Mathematics and its Applications, McGraw-Hill 2003, ISBN 0-07-242434-6This book covers a big part of this lecture.